Answer
a factor
Work Step by Step
Equate $x+2$ to zero then solving for $x$:
\begin{align*}
x+2&=0
\\
x&=-2
.\end{align*}
Substituting $x=
-2
$ in the given expression, $
x^3+4x^2+x-6
,$ results to
\begin{align*}
&
(-2)^3+4(-2)^2+(-2)-6
\\&=
-8+4(4)-2-6
\\&=
-8+16-2-6
\\&=
0
.\end{align*}
Since the substitution above is equal to zero, then the remainder is zero. By the Factor Theorem, $
x+1
$ is a factor of $x^3+4x^2+x-6$.
